Liverpool 4 Chelsea 1: It is now the European Cup or bust for Chelsea, and should they perform this badly against Bayern Munich, bust it will be – or the Europa League, which in owner Roman Abramovich's eyes amounts to the same thing.

Liverpool 4 Chelsea 1: It is now the European Cup or bust for Chelsea, and should they perform this badly against Bayern Munich, bust it will be – or the Europa League, which in owner Roman Abramovich's eyes amounts to the same thing.

Since his takeover in 2003, Stamford Bridge has only ever staged Champions League football. Now, unless they can overcome Bayern in their own stadium, Chelsea will be dipping their toes into some of European football's more distant waters.

There were eight changes last night from the side that had beaten Liverpool in the FA Cup final and they suffered Chelsea's heaviest league defeat of the Abramovich era. Since few of this team are likely to play in the Allianz Arena on 19 May, it would be harsh to read too much into this debacle, although the match climaxed with the Kop chanting: "Bayern Munich, they'll win it five times".

Nothing here would discourage the Germans. Given the suspensions Roberto Di Matteo's side will take into the final, Michael Essien or Florent Malouda may have to be pressed into service in central midfield, where last night they were overrun.

"You have to be objective; we have played 37 games in the Premier League and the points we have lost today are not the reason we have failed to finish fourth," Di Matteo said.

He justified his selection by arguing that, "with everything we have been through we needed to use players who were fresh mentally and physically." They would have been worn down by the finish. John Terry endured such a dreadful first half that someone tweeted Bayern would be appealing to Uefa to have his ban for the final overturned.

Chelsea's situation, however, is identical to Liverpool's when they won the European Cup in Istanbul seven years ago and this was a night that would have made Kenny Dalglish's end-of-season review with the club's owners a little easier. Liverpool began as they had finished the FA Cup final – and that when the season is summed up here will be a matter for lasting regret.

"No, I don't have a feeling of 'what if?'" said Dalglish. "I have a feeling of: 'what a performance'. The last half-hour at Wembley and this performance make up a fantastic two hours of football. The supporters can go away with a smile on their faces."

There were moments last night to give Bayern's representatives pause for thought. Branislav Ivanovic thundered a header against the post when the scores were still level. Fernando Torres, returning to Anfield for the first time since Chelsea made him the Premier League's most expensive footballer, accelerated away from Daniel Agger and sent a shot crashing on to the crossbar beneath the Kop.

Pepe Reina, who has admitted publicly to having endured a poor season, was wrong-footed by Ramires as he met Malouda's free-kick to spark a flicker of a comeback that was extinguished the moment Ross Turnbull sent a clearance straight to Jonjo Shelvey, who drove it back with interest into the net.

That was Liverpool's fourth and final goal, although there might have been more. Just before half-time, Ivanovic barged over Andy Carroll, whom Dalglish thought as unplayable as he had been in the final half hour at Wembley, and conceded a penalty. Stewart Downing has never scored for Liverpool in the league and maintained that record by hitting the post with his kick.

It scarcely seemed to matter. Liverpool were three up and in total command. The rout began with Luis Suarez reaching the byline and pulling the ball back for the approaching figure of Carroll. It missed its target, hit Essien and rolled over the line for the first of three goals in nine minutes.

While Carroll's reputation had been revived by the FA Cup final, Jordan Henderson's had plummeted further. When John W Henry decided to sack Damien Comolli as director of football, the principal complaint was that he had signed players who were wildly overpriced. Henderson, bought from an astonished Sunderland for £20m, was the chief witness for the prosecution.

However when Maxi Rodriguez aimed a loose pass in the general direction of Terry and saw the pillar of Chelsea's defence slip to the floor, Henderson was the one to benefit and you would have had to possess a granite heart not to have willed him to score, which he did in some style.

Carroll may not have scored – however, he contributed to Liverpool's third with surprising delicacy, heading Shelvey's corner across the face of the area for Agger to head home. As he ran towards the Kop in the second half, the great stand stood and chanted his name. It has taken a while but Carroll is becoming the player Dalglish thought him to be.